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     "cell_type": "markdown",
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     "source": [
      "Introduction\n",
      "--------------\n",
      "\n",
      "The Fourier Transform is ubiquitous, but it has singular standing in signal processing because of the way sampling imposes a bandwidth-centric view of the world.  The Discrete Fourier Transform (DFT) is the primary analysis tool for exploring this perspective. Our development unconventionally starts with a matrix/vector representation of the DFT because that facilitates our visual approach which in turn is designed to develop intuition about the operation and usage of the DFT in practice.\n",
      "\n",
      "Let us start with the following DFT matrix\n",
      "\n",
      "$$ \\mathbf{U} = \\frac{1}{\\sqrt N} \\left[ \\exp \\left( j \\frac{2\\pi}{N} n k \\right) \\right]_{n\\in\\{0,N_s-1\\},k\\in\\{0,N-1\\}} $$\n",
      "\n",
      "where $n$ counts rows through the number of samples and $k$ indexes the discrete frequencies as columns. \n",
      "\n",
      "The following figure shows the discrete frequencies on the unit circle and their corresponding real and imaginary parts that are the columns of $\\mathbf{U}$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# must start notebook with --pylab flag\n",
      "\n",
      "from __future__ import  division\n",
      "from matplotlib.patches import FancyArrow\n",
      "import mpl_toolkits.mplot3d.art3d as art3d\n",
      "from mpl_toolkits.mplot3d.art3d import Poly3DCollection\n",
      "import matplotlib.gridspec as gridspec\n",
      "\n",
      "def dftmatrix(Nfft=32,N=None):\n",
      "    'construct DFT matrix'\n",
      "    k= np.arange(Nfft)\n",
      "    if N is None: N = Nfft\n",
      "    n = arange(N)\n",
      "    U = matrix(exp(1j* 2*pi/Nfft *k*n[:,None])) # use numpy broadcasting to create matrix\n",
      "    return U/sqrt(Nfft)\n",
      "\n",
      "Nfft=16\n",
      "v = ones((16,1))\n",
      "U = dftmatrix(Nfft=Nfft,N=16)\n",
      "\n",
      "# --- \n",
      "# hardcoded constants to format complicated figure\n",
      "\n",
      "gs = gridspec.GridSpec(8,12)\n",
      "gs.update( wspace=1, left=0.01)\n",
      "\n",
      "fig =figure(figsize=(10,5))\n",
      "ax0 = subplot(gs[:,:3])\n",
      "fig.add_subplot(ax0)\n",
      "\n",
      "ax0.set_aspect(1)\n",
      "a=2*pi/Nfft*arange(Nfft)\n",
      "\n",
      "colors = ['k','b','r','m','g','Brown','DarkBlue','Tomato','Violet', 'Tan','Salmon','Pink',\n",
      "          'SaddleBrown', 'SpringGreen', 'RosyBrown','Silver',]\n",
      "for j,i in enumerate(a):\n",
      "  ax0.add_patch( FancyArrow(0,0,cos(i),sin(i),width=0.02,\n",
      "                            length_includes_head=True,edgecolor=colors[j]))\n",
      "\n",
      "ax0.text(1,0.1,'0',fontsize=16)\n",
      "ax0.text(0.1,1,r'$\\frac{\\pi}{2}$',fontsize=22)\n",
      "ax0.text(-1,0.1,r'$\\pi$',fontsize=18)\n",
      "ax0.text(0.1,-1.2,r'$\\frac{3\\pi}{2}$',fontsize=22)\n",
      "ax0.axis(array([-1,1,-1,1])*1.45)\n",
      "ax0.set_title('Radial Frequency')\n",
      "ax0.set_xlabel('Real')\n",
      "ax0.set_ylabel('Imaginary')\n",
      "\n",
      "# plots in the middle column\n",
      "for i in range(8):\n",
      "  ax=subplot(gs[i,4:8])\n",
      "  ax.set_xticks([]);  ax.set_yticks([])\n",
      "  ax.set_ylabel(r'$\\Omega_{%d}=%d\\times\\frac{2\\pi}{16}$'%(i,i),fontsize=16,\n",
      "                rotation='horizontal')\n",
      "  ax.plot(U.real[:,i],'-o',color=colors[i])\n",
      "  ax.plot(U.imag[:,i],'--o',color=colors[i],alpha=0.2)\n",
      "  ax.axis(ymax=4/Nfft*1.1,ymin=-4/Nfft*1.1)\n",
      "ax.set_xticks(arange(16))\n",
      "ax.set_xlabel('n')\n",
      "\n",
      "# plots in the far right column\n",
      "for i in range(8):\n",
      "  ax=subplot(gs[i,8:])\n",
      "  ax.set_xticks([]);  ax.set_yticks([])\n",
      "  ax.set_ylabel(r'$\\Omega_{%d}=%d\\times\\frac{2\\pi}{16}$'%(i+8,i+8),fontsize=16,\n",
      "                rotation='horizontal')\n",
      "  ax.plot(U.real[:,i+8],'-o',color=colors[i+8])\n",
      "  ax.plot(U.imag[:,i+8],'--o',color=colors[i+8],alpha=0.2)\n",
      "  ax.axis(ymax=4/Nfft*1.1,ymin=-4/Nfft*1.1)    \n",
      "  ax.yaxis.set_label_position('right')\n",
      "ax.set_xticks(arange(16))\n",
      "ax.set_xlabel('n')\n",
      "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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KlxQSODgQbbGXOkp5HWERWA5bCJ0YijZK61MdTaiGoBuDKFxSSNCIIBSDgrZY62Y8lNXT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X59C4vjJfkjKQ8VfVcefPBB0tLSuHjxosWxFStW8Oyzz7J37166detWZj0Gg4GJEyeityMKyfDh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\nChASiUQikUgkEonEbf4fjHp69VKt6WUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x58b6250>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On the left, the figure shows the discrete frequencies corresponding to each of the columns of the $\\mathbf{U}$ matrix. These are color coded corresponding to the graphs on the right. For example, the $k=1$ column of the $\\mathbf{U}$ matrix (i.e. $ \\mathbf{u}_1 $) corresponds to discrete frequency $\\Omega_1=\\frac{2\\pi}{16}$ marked on the y-axis label which is shown in the second row down the middle column in the figure. The real part of $ \\mathbf{u}_1 $ is plotted in bold and the corresponding imaginary part is plotted semi-transparent because it is just an out-of-phase version of the real part. These real/imaginary parts shown in the graphs correspond to the conjugacy relationships on the leftmost radial plot. For example, $\\Omega_1$ and $\\Omega_{15}$ are complex conjugates and their corresponding imaginary parts are inverted as shown in the plots on the right. \n",
      "\n",
      "The rows of the matrix correspond to the sample index given a particular sampling frequency, $f_s$. This means that if we have $N_s$ samples, then we have sampled a time duration over $N_s/f_s$. However, if we are only given a set of samples without the sampling frequency, then  we can say  nothing about time.  For this reason, you will find discussions based on discrete frequency (i.e. between zero and $2\\pi$) that do not reference  sample rates. Thus, $N$ frequencies either divide the unit circle in discrete frequencies between 0 and $2\\pi$ or divide the sample rate into sampled frequencies between zero and $f_s$. There is a one-to-one relationship between discrete and sampling frequency. In particular, we have for discrete frequency,\n",
      "\n",
      "$$ \\Omega_k = \\frac{2\\pi}{N} k $$\n",
      "\n",
      "and for sampled frequency,\n",
      "\n",
      "$$ f_k = \\frac{f_s}{N} k $$\n",
      "\n",
      "for the same value of $k$. Note that $\\Omega_k$ is periodic with period $N$ (one full turn around the circle). One immediate consequence of the one-to-one correspondence between $\\Omega_k$ and $f_k$ is that when $k=N/2$, we have $\\Omega_{N/2}=\\pi$ (halfway around the circle) and $f_{N/2}=f_s/2$ which is another way of saying that the Nyquist rate (the highest frequency we can unambiguously sample) occurs when $ \\Omega_{N/2} = \\pi$. We can see this by noting that as the discrete frequency rotates counter-clockwise away from zero and towards $\\pi$, the plots on the right get more and more jagged. These also get smoother as the discrete frequency continues to rotate counter-clockwise towards zero again. This is because the higher frequencies are those close to $\\pi$ and the lower frequencies are those close to zero on the complex plane.  We will explore these crucial relationships further later, but for now, let's consider computing the DFT using this matrix."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Computing the DFT\n",
      "--------------------\n",
      "\n",
      "To compute the DFT using the matrix, we calculate the following,\n",
      "\n",
      "$$ \\mathbf{\\hat{x}} = \\mathbf{U}^H \\mathbf{x}$$\n",
      "\n",
      "which individually takes each of the columns of $\\mathbf{U}$ and computes the inner product as the $i^{th}$ entry,\n",
      "\n",
      "$$ \\mathbf{\\hat{x}}_i = \\mathbf{u}_i^H \\mathbf{x}$$\n",
      "\n",
      "That is, we are measuring the *degree of similarity* between each column of $\\mathbf{U}$ and the input vector. We can think of this as the coefficient of the projection of $\\mathbf{x}$ onto  $\\mathbf{u}_i$.\n",
      "\n",
      "We can retrieve the original input from the DFT by calculating\n",
      "\n",
      "$$ \\mathbf{x} = \\mathbf{U} \\mathbf{U}^H \\mathbf{x} $$\n",
      "\n",
      "because the columns of $\\mathbf{U}$ are orthonormal (i.e. $\\mathbf{u}_i^H \\mathbf{u}_j = 0$). An important consequence of this is that $||\\mathbf{x}||=||\\mathbf{\\hat{x}}||$ for any $\\mathbf{x}$.  This is Parseval's theorem and it  means that the DFT is not *stretching* or *distorting* the input which makes it an ideal analysis tool.\n",
      "\n",
      "Zero-Padding and Frequency Sampling\n",
      "------------------------------------------\n",
      "\n",
      "The only relationship between $N$, the size of the DFT, and the number of samples $N_s$ is that $N \\ge N_s$. For implementation reasons, we will always choose $N$ as a power of 2. In the code below, let's now turn to the consquences of choose $N$ much larger that $N_s$. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U = dftmatrix(64,16)\n",
      "x = ones((16,1))\n",
      "X = U.H*x\n",
      "\n",
      "fig,ax=subplots()\n",
      "fig.set_size_inches((8,4))\n",
      "ax.set_aspect(0.8)\n",
      "ax.grid()\n",
      "ax.plot(arange(0,64)*2*pi/64.,abs(X),'o-')\n",
      "ax.set_ylabel(r'$|X(\\Omega)|$',fontsize=18)\n",
      "ax.set_xticks([0, pi/2., pi, 3*pi/2,2*pi])\n",
      "ax.set_xlabel(r'$\\Omega$',fontsize=16)\n",
      "ax.axis([0, 2*pi,0,2.1])\n",
      "ax.set_xticklabels(['0',r'$\\frac{\\pi}{2}$', r'$\\pi$',r'$\\frac{3\\pi}{2}$', r'$2\\pi$'],\n",
      "                   fontsize=18);\n",
      "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "[<matplotlib.text.Text at 0x69ad330>,\n",
        " <matplotlib.text.Text at 0x69a1070>,\n",
        " <matplotlib.text.Text at 0x5489af0>,\n",
        " <matplotlib.text.Text at 0x5489f90>,\n",
        " <matplotlib.text.Text at 0x57f5450>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nzpwRwcHBRteNHDlS5OTk6JeHDBki9u/fX2U7M95OjaZMEWLhwlrvhqywfft2uUMgK7Hu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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x5d8ea10>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As you may recall from our [earlier discussion](http://python-for-signal-processing.blogspot.com/2012/09/investigating-sampling-theorem-in-this.html), this plot looks suspiciously like the `sinc` function. If you've been following closely, you may realize that for the above example we had $\\mathbf{x}=\\mathbf{1}$. But isn't this one of the columns of the $\\mathbf{U}$ matrix? If all the columns of that matrix are orthonormal, then why is there is more than one non-zero point on this graph? The subtle point here is that the DFT matrix has dimensions $64 \\times 16$. This means that computationally,\n",
      "\n",
      "$$ \\mathbf{U}_{16\\times64}^H \\mathbf{x} = \\mathbf{U}_{64\\times64}^H \\left[\\mathbf{x},\\mathbf{0}\\right]^T$$\n",
      "\n",
      "In other words, filling the original $16\\times 1$ vector $\\mathbf{x}$ with zeros and using a larger compatible $\\mathbf{U}_{64\\times64}$ matrix has the same effect as using the $\\mathbf{U}_{16\\times64}$ matrix. The answer to the question is therefore that $\\mathbf{x} = \\mathbf{1}_{16\\times1} \\ne \\left[ \\mathbf{1}_{16\\times1},\\mathbf{0}\\right]^T$ and the zero-augmented ones vector is *not* orthnormal to any columns in $\\mathbf{U}_{64\\times64}$.  This explains why there are so many non-zero points on the graph at different discrete frequencies.\n",
      "\n",
      "Let's drive this point home in the next figure."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U = dftmatrix(64,16)\n",
      "x = ones((16,1))\n",
      "X = U.H*x\n",
      "\n",
      "fig,ax=subplots()\n",
      "fig.set_size_inches((8,4))\n",
      "\n",
      "ax.set_aspect(0.8)\n",
      "ax.grid()\n",
      "ax.plot(arange(0,64)*2*pi/64.,abs(X),'o-',label='zero padded')\n",
      "ax.stem(arange(0,16)*2*pi/16.,abs(dftmatrix(16).H*x),\n",
      "        markerfmt='gs', basefmt='g-',linefmt='g-',\n",
      "        label='no padding')\n",
      "ax.set_ylabel(r'$|X(\\Omega)|$',fontsize=18)\n",
      "ax.set_xticks([0, pi/2., pi, 3*pi/2,2*pi])\n",
      "ax.axis([-.1, 2*pi,-.1,4.1])\n",
      "ax.legend(loc=0)\n",
      "ax.set_xticklabels(['0',r'$\\frac{\\pi}{2}$', r'$\\pi$',r'$\\frac{3\\pi}{2}$', r'$2\\pi$'],\n",
      "                   fontsize=18);\n",
      "ax.set_title('Zero padding samples more frequencies');\n",
      "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "<matplotlib.text.Text at 0x6a33650>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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h7969+PnnnzFx4kRjh6XE9LusGWOMGZXQxmJVuXXrFp588kkUFhaie/fu+Pzz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\nfkLWEo8jM8YYa4oxuquBtpC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       "text": [
        "<matplotlib.figure.Figure at 0x57f5390>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the figure above, without zero-padding, $\\mathbf{x}$ is the $ 0^{th} $ column of the 16-point DFT matrix and so all the coefficients except for the $0^{th}$ column are zero due to orthonormality (shown by the green squares).  But, the zero-padded 64-element-long $\\mathbf{x}$ vector is definitely *not* a column of the 64-point DFT matrix so we would *not* expect all the other terms to be zero. In fact, the other terms account for the 64 discrete frequencies that are plotted above. This means that zero-padding $\\mathbf{x}$ and using the 64-point DFT matrix analyzes the signal across more frequencies. \n",
      "\n",
      "Notice that for the $ 0^{th}$ frequency the height of the DFT magnitude is different for the zero-padded constant signal compared to the unpadded version. Recall from Parseval's theorem that $ ||\\mathbf{x}||=||\\mathbf{\\hat{x}}|| $ but this does not account for how the signal may be spread across frequency. In the unpadded case, *all* of the signal energy is concentrated in the $ \\mathbf{u}_0 $ column of the DFT matrix because our constant signal is just a scalar multiple of $ \\mathbf{u}_0 $. In the padded case, the signal's energy is spread out across more frequencies with smaller signal magnitudes per frequency, thus satisfying Parseval's theorem. In other words, the single non-zero term in the unpadded DFT is smeared out over all the other frequencies in the padded case.\n",
      "\n",
      "The problem with the figure shown is that it does not emphasize that the discrete frequencies are periodic with period $N$. The following figure below plots the 64-point DFT on the face of a cylinder to emphasize the periodicity of the discrete frequencies."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a=2*pi/64.*arange(64)\n",
      "d=vstack([cos(a),sin(a),array(abs(X)).flatten()]).T\n",
      "\n",
      "fig = plt.figure()\n",
      "fig.set_size_inches(6,6)\n",
      "ax = fig.add_subplot(1, 1, 1, projection='3d')\n",
      "ax.axis([-1,1,-1,1])\n",
      "ax.set_zlim([0,d[:,2].max()])\n",
      "ax.set_aspect(1)\n",
      "ax.view_init(azim=-30)\n",
      "\n",
      "ax.set_xlabel('real')\n",
      "ax.set_ylabel('imag')\n",
      "ax.set_zlabel('Abs')\n",
      "ax.set_title('64-Point DFT Magnitudes')\n",
      "\n",
      "def facet_filled(x,alpha=0.5,color='b'):\n",
      "    'construct 3D facet from adjacent points filled to zero'\n",
      "    a,b=x\n",
      "    a0= a*array([1,1,0])\n",
      "    b0= b*array([1,1,0])\n",
      "    ve = vstack([a,a0,b0,b])      # create closed polygon facet\n",
      "    poly = Poly3DCollection([ve]) # create facet\n",
      "    poly.set_alpha(alpha)\n",
      "    poly.set_color(color)\n",
      "    return poly\n",
      "\n",
      "sl=[slice(i,i+2) for i in range(d.shape[0]-2)] # collect neighboring points\n",
      "for s in sl:\n",
      "  poly=facet_filled(d[s,:])\n",
      "  ax.add_collection3d(poly)\n",
      " \n",
      "# edge polygons    \n",
      "ax.add_collection3d(facet_filled(d[[-1,0],:]))\n",
      "ax.add_collection3d(facet_filled(d[[-2,-1],:]))\n",
      "\n",
      "# add 0 and pi/2 arrows for reference\n",
      "a=FancyArrow(0,0,1,0,width=0.02,length_includes_head=True)\n",
      "ax.add_patch(a)\n",
      "b=FancyArrow(0,0,0,1,width=0.02,length_includes_head=True)\n",
      "ax.add_patch(b)\n",
      "art3d.patch_2d_to_3d(a)\n",
      "art3d.patch_2d_to_3d(b)\n",
      "# fig.savefig('figure_00@.png', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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k15TlLWoURRElC6sEj+nl0Q2EkHEpxMLd0DgI0Z0gWEWW//AiMZmiC3h4VzaRdblc8Hq9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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x6b795f0>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The figure above is very important and we will be using it as a glyph in the following. It shows the same magnitude of the $X(\\Omega)$ 64-point DFT as before, but now that it is plotted on a cylinder, we can really see the periodic discrete frequencies. The two arrows in the xy-plane show the discrete frequencies zero and $\\pi/2$ for reference.  \n",
      "\n",
      "We will need the following setup code below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def drawDFTView(X,ax=None,fig=None):\n",
      "    'above code as a function. Draws 3D diagram given DFT matrix'\n",
      "    a=2*pi/len(X)*arange(len(X))\n",
      "    d=vstack([cos(a),sin(a),array(abs(X)).flatten()]).T\n",
      "    if ax is None and fig is None:\n",
      "        fig = plt.figure()\n",
      "        fig.set_size_inches(6,6)\n",
      "        \n",
      "    if ax is None: # add ax to existing figure\n",
      "        ax = fig.add_subplot(1, 1, 1, projection='3d')\n",
      "        \n",
      "    ax.axis([-1,1,-1,1])\n",
      "    ax.set_zlim([0,d[:,2].max()])\n",
      "    ax.set_aspect(1)\n",
      "    ax.view_init(azim=-30)\n",
      "    a=FancyArrow(0,0,1,0,width=0.02,length_includes_head=True)\n",
      "    ax.add_patch(a)\n",
      "    b=FancyArrow(0,0,0,1,width=0.02,length_includes_head=True)\n",
      "    ax.add_patch(b)\n",
      "    art3d.patch_2d_to_3d(a)\n",
      "    art3d.patch_2d_to_3d(b)\n",
      "    #ax.set_xticks([])\n",
      "    #ax.set_yticks([])\n",
      "    #ax.set_zticks([])\n",
      "    ax.axis('off')\n",
      "\n",
      "    sl=[slice(i,i+2) for i in range(d.shape[0]-2)] # collect neighboring points\n",
      "    for s in sl:\n",
      "      poly=facet_filled(d[s,:])\n",
      "      ax.add_collection3d(poly)\n",
      "     \n",
      "    # edge polygons    \n",
      "    ax.add_collection3d(facet_filled(d[[-1,0],:]))\n",
      "    ax.add_collection3d(facet_filled(d[[-2,-1],:]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def drawInOut(X,v,return_axes=False):\n",
      "    fig = plt.figure()\n",
      "    fig.set_size_inches(8,8)\n",
      "    gs = gridspec.GridSpec(8,6)\n",
      "        \n",
      "    ax1 = plt.subplot(gs[3:5,:2])\n",
      "    ax2 = plt.subplot(gs[:,2:],projection='3d')\n",
      "    \n",
      "    ax1.stem(arange(len(v)),v)\n",
      "    ymin,ymax= ax1.get_ylim()\n",
      "    ax1.set_ylim(ymax = ymax*1.2, ymin = ymin*1.2)\n",
      "    ax1.set_title('input signal')\n",
      "    ax1.set_xlabel('time sample index')\n",
      "    ax1.tick_params(labelsize=8)\n",
      "    \n",
      "    drawDFTView(X,ax2)\n",
      "    if return_axes:\n",
      "        return ax1,ax2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Real Signals and DFT Symmetry\n",
      "-----------------------------------\n",
      "\n",
      "Note the symmetric lobes in the following figure showing the DFT of a real signal. The plot on the left is the signal in the sampled time-domain and the plot on the right is its DFT-magnitude glyph."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "v = U[:,6].real\n",
      "ax=drawInOut(U.H*v,v,return_axes=True)\n",
      "# ax.figure.savefig('figure_00@.png', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SuthYcV23aeP6OKNR8qT//NOWLuUOTy56ZelWVAC//ur6czqybp0IZ9eurte3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\nMCNnAJiRMwDMBBwh/bPcHnoaAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x54819d0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Because the input signal is real, the DFT is symmetric. To see this, recall that in our first figure we observed for every $\\mathbf{u}_i$, we had its complex  conjugate $\\mathbf{u}_{N-i}$ and since the real parts of complex conjugates are the same and there is no imaginary part in the input signal, the resulting corresponding inner products are complex conjugates and thus have the same magnitudes.\n",
      "\n",
      "The next block of code illustrates this."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print abs(U[:,[6,64-6]].H*v) # real signal has same abs() inner product for conjugate columns"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 0.125]\n",
        " [ 0.125]]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This fact has extremely important computational consequences for the fast implemention of the DFT (i.e. FFT), which we will take up another time. For now, it's enough to recognize the symmetry of the DFT of real signals. \n",
      "\n",
      "High/Low-Frequency Signals and Their DFTs\n",
      "-----------------------------------------------\n",
      "\n",
      "Now that we have all the vocabulary defined, we can ask one more intuitive question: what does the highest frequency signal (i.e. $\\Omega_{N/2}=\\pi$) look like in the sampled time-domain? This is shown in the top figure below that shows a signal toggling back and forth positive and negative. Note that the amplitudes of this toggling are not important, it's just the *rate* of toggling that defines the high frequency signal. Also, what does the lowest frequency signal (i.e. $\\Omega_0=0$) look like as a sampled signal? This is shown in the bottom figure. Note that it is the mirror image of the high frequency signal.\n",
      "\n",
      "I invite you to please download the [IPython notebook corresponding to this post ](https://github.com/unpingco/Python-for-Signal-Processing/blob/master/Fourier_Transform.ipynb) and play with these plots to develop an intuition for where the various input signals appear."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "v = matrix(cos(pi*arange(0,16))).T\n",
      "ax1,ax2=drawInOut(U.H*v,v,return_axes=1)\n",
      "ax1.set_title('Highest Frequency')\n",
      "# ax1.figure.savefig('figure_00@.png', bbox_inches='tight', dpi=300)\n",
      "\n",
      "v = ones((16,1))\n",
      "ax1,ax2=drawInOut(U.H*v,v,return_axes=1)\n",
      "ax1.set_title('Lowest Frequency')\n",
      "# ax1.figure.savefig('figure_00@.png', bbox_inches='tight', dpi=300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<matplotlib.text.Text at 0x71370f0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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P+fjIIKq0NPNt27YBFhvKlRvE9o5bPl9EhAzays21ff/0dODbb6VZ3NZ5Lc8Z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\nyIC5D7k8RqP0pX71lYTNwIG272syyQ5CX30lteA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       "text": [
        "<matplotlib.figure.Figure at 0x58b6210>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SU4GyMiAwsOYxe4Gr18tCGAzcxoWBS0TUSFVXAx98IMs42mIw1OzDVe/X62VkMzUeDFwi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\nYeLEiRg8eDDatWtnfNxzzz2H6upqxMT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       "text": [
        "<matplotlib.figure.Figure at 0x70d4270>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Summary"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this section, we considered the Discrete Fourier Transform (DFT) using a matrix/vector approach. We used this approach to  develop an intuitive visual vocabulary for the DFT with respect to high/low frequency  and real-valued signals. We used zero-padding to enhance frequency domain signal analysis.\n",
      "\n",
      "As usual, the corresponding IPython notebook for this post  is available for download [here](https://github.com/unpingco/Python-for-Signal-Processing/blob/master/Fourier_Transform.ipynb). \n",
      "\n",
      "Comments and corrections welcome!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "References\n",
      "---------------\n",
      "\n",
      "* Oppenheim, A. V., and A. S. Willsky. \"Signals and Systems.\" Prentice-Hall, (1997)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%qtconsole"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    }
   ],
   "metadata": {}
  }
 ]
}